COURSE INFORMATION, PHYSICS 722, ADVANCED CLASSICAL THEORETICAL PHYSICS

Send comments or questions to: ldurand@theory2.physics.wisc.edu

COURSE INFORMATION

PHYSICS 722, ADVANCED CLASSICAL THEORETICAL PHYSICS

SPRING, 1999

Instructor:

L. Durand, 4209 Chamberlin.
Email address: ldurand@theory2.physics.wisc.edu
Web site: http://theory1.physics.wisc.edu/~ldurand/
Telephone: 262--3996.

Meets:

11:00 MWF, 1327 Sterling Hall

Office hours:

I'm around most of the time. Feel free to stop in with questions or comments (except the hour before class!), or check after class, by email, etc., for a definite time to come by.

Objectives of the course:

A great deal of very interesting and important physics in the general areas of dynamics and electrodynamics is not covered in the graduate courses Physics 711 and 721, respectively. The "missing" material on electrodynamics and continuum problems (classical fields) is particularly important and of wide applicability. Many of the applications are to material that "every physicist is expected to know" (so come learn it!).

My basic objective in Physics 722 is to extend the coverage of electrodynamics and dynamics as described below, treat important physics applications, and give the the students in the course enough background in these classical areas that they will recognize the nature of a problem encountered in their own research activities, and will know how to attack it. In addition, the problems we will study will often provide insight into related quantum mechanical problems. I like also to make contact with modern mathematical approaches, especially in mechanics, when these are illuminating for the physics.

Course content:

Slightly more than half the course will be concerned with the material in Chaps. 11--15 of J.D. Jackson's Classical Electrodynamics, 3rd edition, and related subjects, mainly material concerned with relativistic particle electrodynamics and radiation, e.g., relativity, invariants of the electromagnetic field, the fields of relativistic particles, collisions, interactions of particles in matter, energy loss, Cherenkov and transition radiation, radiation by accelerated particles, bremsstrahlung and the method of virtual quanta.

The remainder of the course will cover selected topics in mechanics that have wide applicability, e.g., classical field theory, perturbations, adiabatic variation of parameters, invariants and symmetries, symplectic transformations and mappings, and stability, with examples in continuum and particle mechanics, accelerator physics, and elsewhere.

Texts:

J.D. Jackson, Classical Electrodynamics, 3rd edition, H. Goldstein, Classical Mechanics, 2nd edition, plus selected readings in books on reserve in the Physics Library (see the comments below).

Note the switch to the 3rd edition of Jackson! This incorporates material that appeared in 722 in the past only in my notes and homework problems. For example, the basic physics of undulators in synchrotron radiation devices was covered last year homework problems LD6 and LD8, but now occupies Sec. 14.7 in Jackson. Since Jackson has become a basic reference, the fact that the new edition also uses SI units in Chaps. 1-10 might make you happy!

Homework:

The course is problem-based, and there will be problem sets most weeks. The problems are often challenging, but are directed to real, often current, physical applications, so are correspondingly interesting.

You are strongly encouraged to discuss the problem assignments with other students in the class, and to work together on their solution. I am happy to discuss the problems with you and give hints, but you may learn more from your fellow students! Most physics is done in collaborations, and this will give you a chance to develop the skills in working on real problems in a collaborative setting which are expected by most potential employers of physicists.

I will put problem solutions on reserve in the Physics Library after the due date. Be sure to look at the solutions: I often add extra remarks on the physics involved there or on the web version of the problems.

Exams and grades:

The problem grade will count as 40% (40 points) of the final grade (free points if you do the work!). There will be two hour exams in class during the semester, probably FRIDAY, FEBRUARY 26 and FRIDAY, APRIL 16, and a final exam at 12:25 pm MONDAY, MAY 10. Each will count 20 points in the final grade.

My grading scale for this course is normally 87-100 for A, 70-86 B, 60-69 C, with AB used in the area approaching the B to A transition. I don't raise the cutoffs, but may dip below the levels stated if an exam turns out to be too hard, if a person started poorly but demonstrated real improvement during the semester, or in other exceptional circumstances.

References on reserve in the Physics Library, 4220 Chamberlin

Electrodynamics

L.D. Landau and E.M. Lifshitz, Classical Theory of Fields: one of the classic texts, good on relativistic electrodynamics, etc., also introduces general relativity which we will not cover.
L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media: interesting treatments of relativistic particles in matter, nonlinear wave effects.
W. Thirring, Classical Field Theory: a mixture of electrodynamics, general relativity, with good applications to radiation from particles, diffraction theory.

Mechanics

V.I. Arnol'd, Mathematical Methods of Classical Mechanics: classical mechanics from an advanced point of view, excellent on the foundations of Hamiltonian mechanics---``reads PG, should be rated X'' (L. Leavitt).
A.L. Fetter and J.D. Walecka, Theoretical Mechanics of Particles and Continua: good on continuum mechanics, classical fields.
L.A. Pars, Analytical Dynamics: a modern treatise on dynamics, complete expositions of many alternative approaches, especially good on motions in the neighborhood of a given motion and near singular points.
W. Thirring, Classical Dynamical Systems: mathematical approach to dynamics by a physicist.
E.T. Whittaker, Analytical Dynamics: the classic treatise, contains most results up to modern topological work, but often expressed in older forms; well worth studying.

Other books of interest:

G.B. Whitham, Linear and Nonlinear Waves: wonderful collection of material on waves, i.e., classical fields.
F. Gantmacher, Lectures in Analytical Mechanics: excellent little book, good on invariants, canonical transformations, stability and oscillation problems. Symplectic transformations are called ``simplicial'' in this book, a mistranslation from the Russian.
E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: emphasizes groups and algebraic structures, good on constrained Hamiltonian systems and Dirac brackets.
R. Abraham and J.E. Marsden, Foundations of Mechanics: mathematical foundations of mechanics, modern topological and differentiable dynamics from a mathematician's point of view---familiar examples may be hard to recognize!
Send comments or questions to: ldurand@theory2.physics.wisc.edu
© 1997, 1998, Loyal Durand